17-animal inheritance puzzle
The 17-animal inheritance puzzle is a mathematical puzzle involving unequal but fair allocation of indivisible goods, usually stated in terms of inheritance of a number of large animals (17 camels, 17 horses, 17 elephants, etc.)
Despite often being framed as a puzzle, it is more an anecdote about a curious calculation than a problem with a clear mathematical solution.
Instead, a version of the puzzle can be traced back to the works of Mulla Muhammad Mahdi Naraqi, an 18th-century Iranian philosopher.
[2] As usually stated, to solve the puzzle, the three sons ask for the help of another man, often a priest, judge, or other local official.
Some sources point out an additional feature of this solution: each son is satisfied, because he receives more camels than his originally-stated inheritance.
[3] Similar problems of unequal division go back to ancient times, but without the twist of the loan and return of the extra camel.
For instance, the Rhind Mathematical Papyrus features a problem in which many loaves of bread are to be divided in four different specified proportions.
[2][4] The 17 animals puzzle can be seen as an example of a "completion to unity" problem, of a type found in other examples on this papyrus, in which a set of fractions adding to less than one should be completed, by adding more fractions, to make their total come out to exactly one.
[9] Supposed origins of the problem in the works of al-Khwarizmi, Fibonacci or Tartaglia also cannot be verified.
[10] A "legendary tale" attributes it to 16th-century Mughal Empire minister Birbal.
[9] By 1850 it had already entered circulation in America, through a travelogue of Mesopotamia published by James Phillips Fletcher.
[12][13] It appeared in The Mathematical Monthly in 1859,[10][14] and a version with 17 elephants and a claimed Chinese origin was included in Hanky Panky: A Book of Conjuring Tricks (London, 1872), edited by William Henry Cremer but often attributed to Wiljalba Frikell or Henry Llewellyn Williams.
[2][10] The same puzzle subsequently appeared in the late 19th and early 20th centuries in the works of Henry Dudeney, Sam Loyd,[2] Édouard Lucas,[9] Professor Hoffmann,[15] and Émile Fourrey,[16] among others.
[22][23] Another variant of the puzzle appears in the book The Man Who Counted, a mathematical puzzle book originally published in Portuguese by Júlio César de Mello e Souza in 1938.
The endnotes to the English translation of the book cite the 17-camel version of the problem to the works of Fourrey and Gaston Boucheny (1939).
[29] Paul Stockmeyer, a computer scientist, defines a class of similar puzzles for any number
) form the integer sequence S. Naranan, an Indian physicist, seeks a more restricted class of generalized puzzles, with only three terms, and with
[11] Brazilian researchers Márcio Luís Ferreira Nascimento and Luiz Barco generalize the problem further, as in the variation with 35 camels, to instances in which more than one camel may be lent and the number returned may be larger than the number lent.
